Generally, the cooling of a vehicle compartment (i.e. passenger compartment of a vehicle) is carried out in one of the following two ways. That is, one is decreasing the temperature of the vehicle compartment, while the other is keeping a comfortable low temperature in the vehicle compartment. While decreasing the temperature, the compressor of an air-conditioning system of a vehicle has to exert a high cooling performance, and while maintaining a comfortable low temperature, the compressor has to exert a rather low cooling performance. In the conventional air-conditioning system of a vehicle, a compressor having as large as possible cooling capacity permitted by the vehicle's engine performance is often employed for satisfying the requirement for a rapid cooling of the vehicle compartment. Therefore, while the vehicle is driven under a normal running state and while the vehicle compartment is cooled so as to be kept at a comfortable low temperature, the cooling capacity of the compressor is excessively large with respect to the cooling load. As a result, the compressor per se must be driven under a rather low cooling load. Accordingly, during the operation of the compressor, the volumetric efficiency of the compressor must be low. Further, a clutch that is arranged between the vehicle engine and the compressor must often be connected and disconnected. This operation causes the clutch to wear out rapidly. Moreover, everytime the clutch is disconnected and connected, a large starting torque is necessary for starting the compressor. That is, a large change in the driving torque of the compressor occurs. This fact adversely affects comfortable driving of the vehicle. Further, when a compressor is started, there sometimes occurs a liquid compression which deteriorates the durability of the compressor, if the volume of the exhaust chamber of the compressor is rather small. In addition, such liquid compression causes the generation of loud noise. In some de-luxe cars, the conventional compressor of the air-conditioning system is continuously driven, and the amount of the refrigerant gas coming into the compressor is controlled by a pressure control valve arranged adjacent to the outlet of an evaporator of the air conditioning system. If the car compartment is excessively cooled, the air is heated up to an appropriate temperature and is blown into the compartment. This method is therefore extremely uneconomical.